Nonlinear Dynamics And Chaos
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Nonlinear Dynamics and Chaos
Author | : Steven H. Strogatz |
Publsiher | : CRC Press |
Total Pages | : 532 |
Release | : 2018-05-04 |
Genre | : Mathematics |
ISBN | : 9780429961113 |
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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Nonlinear Dynamics and Chaos
Author | : Steven H. Strogatz |
Publsiher | : Hachette UK |
Total Pages | : 614 |
Release | : 2014-08-26 |
Genre | : Mathematics |
ISBN | : 9780813349114 |
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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.
Nonlinear Dynamics and Chaos
Author | : Steven H Strogatz |
Publsiher | : CRC Press |
Total Pages | : 616 |
Release | : 2024-01-16 |
Genre | : Mathematics |
ISBN | : 9780429676284 |
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The goal of this Third Edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Chemistry, and Engineering is the same as previous editions: to provide a good foundation — and a joyful experience! — for anyone who’d like to learn about nonlinear dynamics and chaos from an applied perspective. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, strange attractors, and synchronization. The prerequisites are comfort with multivariable calculus and linear algebra, as well as a first course in physics. Changes to this edition include substantial exercises about conceptual models of climate change, an updated treatment of the SIR model of epidemics, and amendments (based on recent research) on the Selkov model of oscillatory glycolysis. Equations, diagrams, and explanations have been reconsidered and often revised. There are also about 50 new references, many from the recent literature. The most notable change is a new chapter about the Kuramoto model. This icon of nonlinear dynamics, introduced in 1975 by the Japanese physicist Yoshiki Kuramoto, is one of the rare examples of a high-dimensional nonlinear system that can be solved by elementary means. It provides an entrée to current research on complex systems, synchronization, and networks, yet is accessible to newcomers. Students and teachers have embraced the book in the past for its exceptional clarity and rich applications, and its general approach and framework continue to be sound.
Nonlinear Dynamics and Chaos
Author | : J. M. T. Thompson,H. B. Stewart |
Publsiher | : John Wiley & Sons |
Total Pages | : 492 |
Release | : 2002-02-15 |
Genre | : Science |
ISBN | : 0471876844 |
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Ein angesehener Bestseller - jetzt in der 2.aktualisierten Auflage! In diesem Buch finden Sie die aktuellsten Forschungsergebnisse auf dem Gebiet nichtlinearer Dynamik und Chaos, einem der am schnellsten wachsenden Teilgebiete der Mathematik. Die seit der ersten Auflage hinzugekommenen Erkenntnisse sind in einem zusätzlichen Kapitel übersichtlich zusammengefasst.
Chaos and Nonlinear Dynamics
Author | : Robert C. Hilborn |
Publsiher | : Unknown |
Total Pages | : 676 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0198507232 |
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This book introduces readers to the full range of current and background activity in the rapidly growing field of nonlinear dynamics. It uses a step-by-step introduction to dynamics and geometry in state space to help in understanding nonlinear dynamics and includes a thorough treatment of both differential equation models and iterated map models as well as a derivation of the famous Feigenbaum numbers. It is the only introductory book available that includes the important field of pattern formation and a survey of the controversial questions of quantum chaos. This second edition has been restructured for easier use and the extensive annotated references are updated through January 2000 and include many web sites for a number of the major nonlinear dynamics research centers. With over 200 figures and diagrams, analytic and computer exercises this book is a necessity for both the classroom and the lab.
Nonlinear Dynamics and Chaos
Author | : Steven H. Strogatz |
Publsiher | : CRC Press |
Total Pages | : 533 |
Release | : 2018-05-04 |
Genre | : Mathematics |
ISBN | : 9780429972195 |
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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Nonlinear Dynamics Chaos and Instability
Author | : William A. Brock,David Arthur Hsieh,Blake Dean LeBaron |
Publsiher | : MIT Press |
Total Pages | : 362 |
Release | : 1991 |
Genre | : Business & Economics |
ISBN | : 0262023296 |
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Brock, Hsieh, and LeBaron show how the principles of chaos theory can be applied to such areas of economics and finance as the changing structure of stock returns and nonlinearity in foreign exchange.
Student Solutions Manual for Nonlinear Dynamics and Chaos 2nd edition
Author | : Mitchal Dichter |
Publsiher | : CRC Press |
Total Pages | : 305 |
Release | : 2018-05-15 |
Genre | : Mathematics |
ISBN | : 9780429972638 |
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This official Student Solutions Manual includes solutions to the odd-numbered exercises featured in the second edition of Steven Strogatz's classic text Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. The textbook and accompanying Student Solutions Manual are aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. Complete with graphs and worked-out solutions, this manual demonstrates techniques for students to analyze differential equations, bifurcations, chaos, fractals, and other subjects Strogatz explores in his popular book.